This Week’s Finds (Week 317)

Anyone seriously interested in global warming needs to learn about the ‘ice ages’, or more technically ‘glacial periods’. After all, these are some of the most prominent natural variations in the Earth’s temperature. And they’re rather mysterious. They could be caused by changes in the Earth’s orbit called Milankovich cycles… but the evidence is not completely compelling. I want to talk about that.

But to understand ice ages, the first thing we need to know is that the Earth hasn’t always had them! The Earth’s climate has been cooling and becoming more erratic for the last 35 million years, with full-blown glacial periods kicking in only about 1.8 million years ago.

So, this week let’s start with a little tour of the Earth’s climate history. Somewhat arbitrarily, let’s begin with the extinction of the dinosaurs about 65 million years ago. Here’s a graph of what the temperature has been doing since then:

Of course you should have lots of questions about how this graph was made, and how well we really know these ancient temperatures! But for now I’m just giving a quick overview—click on the graphs for more. In future weeks I should delve into more technical details.

The Paleocene began with a bang, as an asteroid 10 kilometers across hit the Gulf of Mexico in an explosion two million times larger than the biggest nuclear weapon ever detonated. A megatsunami thousands of meters high ripped across the Atlantic, and molten quartz hurled high into the atmosphere ignited wildfires over the whole planet. A day to remember, for sure.

The Earth looked like this back then:

The Paleocene started out hot: the ocean was 10° to 15° Celsius warmer than today. Then it got even hotter! Besides a gradual temperature rise, at the very end of this epoch there was a drastic incident called the Paleocene-Eocene Thermal Maximum— that’s the spike labelled "PETM". Ocean surface temperatures worldwide shot up by 5-8°C for a few thousand years—but in the Arctic, it heated up even more, to a balmy 23°C. This caused a severe dieoff of little ocean critters called foraminifera, and a drastic change of the dominant mammal species. What caused it? That’s a good question, but right now I’m just giving you a quick tour.

During the Eocene, temperatures continued to rise until the so-called ‘Eocene Optimum’, about halfway through. Even at the start, the continents were close to where they are now—but the average annual temperature in arctic Canada and Siberia was a balmy 18 °C. The dominant plants up there were palm trees and cycads. Fossil monitor lizards (sort of like alligators) dating back to this era have been found in Svalbard, an island north of Greenland that’s now covered with ice all year. Antarctica was home to cool temperate forests, including beech trees and ferns. In particular, our Earth had no permanent polar ice caps!

Life back then was very different. The biggest member of the order Carnivora, which now includes dogs, cats, bears, and the like, was merely the size of a housecat. The largest predatory mammals were of another, now extinct order: the creodonts, like this one drawn by Dmitry Bogdanov:

But the biggest predator of all was not a mammal: it wasDiatryma, the 8-foot tall "terror bird", with a fearsome beak!

As the Eocene drew to a close, temperatures began to drop. And at the start of the Oligocene, they plummeted! Glaciers started forming in Antarctica. The growth of ice sheets led to a dropping of the sea level. Tropical jungles gave ground to cooler woodlands.

What caused this? That’s another good question. Some seek the answer in plate tectonics. The Oligocene is when India collided with Asia, throwing up the Himalayas and the vast Tibetan plateau. Some argue this led to a significant change in global weather patterns. But this is also the time when Australia and South America finally separated from Antarctica. Some argue that the formation of an ocean completely surrounding Antarctica led to the cooling weather patterns. After all, that lets cold water go round and round Antarctica without ever being driven up towards the equator.

Near the end of the Oligocene temperatures shot up again and the Antarctic thawed. Then it cooled, then it warmed again… but by the middle of the Miocene, temperatures began to drop more seriously, and glaciers again formed on the Antarctic. It’s been frozen ever since. Why all these temperature fluctuations? That’s another good question.

The Miocene is when grasslands first became common. It’s sort of amazing that something we take so much for granted—grass—can be so new! But grasslands, as opposed to thicker forests and jungles, are characteristic of cooler climates. And as Nigel Calder has suggested, grasslands were crucial to the development of humans! Early hominids lived on the border between forests and grasslands. That has a lot to do with why we stand on our hind legs and have hands rather than paws. Much later, the agricultural revolution relied heavily on grasses like wheat, rice, corn, sorghum, rye, and millet. As we ate more of these plants, we drastically transformed them by breeding, and removed forests to grow more grasses. In return, the grasses drastically transformed us: the ability to stockpile surplus grains ended our hunter-gatherer lifestyle and gave rise to cities, kingdoms, and slave labor.

So, you could say we coevolved with grasses!

Indeed, the sequence of developments leading to humans came shortly after the rise of grasslands. Apes split off from monkeys 21 million years ago, in the Miocene. The genus Homo split off from other apes like gorillas and chimpanzees 5 million years ago, near the beginning of the Pliocene. The fully bipedal Homo erectus dates back to 1.9 million years ago, near the end of the Pliocene. But we’re getting ahead of ourselves…

Starting around the Pliocene, the Earth’s temperature has been getting every more jittery as it cools. Something is making the temperature unstable! And these fluctuations are not just getting more severe—they’re also lasting longer.

These temperature fluctuations are far from being neatly periodic, despite the optimistic labels on the above graph saying “41 kiloyear cycle” and “100 kiloyear cycle”. And beware: the data in the above graph was manipulated so it would synchronize with the Milankovitch cycles! Is that really justified? Do these cycles really cause the changes in the Earth’s climate? More good questions.

Here’s a graph that shows more clearly the noisy nature of the Earth’s climate in the last 7 million years:

You can tell this graph was made by a real paleontologist, because they like to put the present on the left instead of on the right.

And maybe you’re getting curious about this “δ18O benthic carbonate” business? Well, we can’t directly measure the temperatures long ago by sticking a thermometer into an ancient rock! We need to use ‘climate proxies’: things we can measure now, that we believe are correlated to features of the climate long ago. δ18O is the change in the amount of oxygen-18 (a less common, heavier isotope of oxygen) in carbonate deposits dug up from ancient ocean sediments. These deposits were made by foraminifera and other tiny ocean critters. The amount of oxygen-18 in these deposits is used as temperature proxy: the more of it there is, the colder we think it was. Why? That’s another good question.

By the beginning of the Pleistocene, the Earth’s jerky temperature variations became full-fledged ‘glacial cycles’. In the last million years there have been about ten glacial cycles, though it’s hard to count them in any precise way—it’s like counting mountains in a mountain range:

Now the present is on the right again—but just to keep you on your toes, here up means cold, or at least more oxygen-18. I copied this graph from:

We can get some more detail on the last four glacial periods from the change in the amount of deuterium in Vostok and EPICA ice core samples, and also changes in the amount of oxygen-18 in foraminifera (that’s the graph labelled ‘Ice Volume’):

As you can see here, the third-to-last glacial ended about 380,000 years ago. In the warm period that followed, the first signs of Homo neanderthalensis appear about 350,000 years ago, and the first Homo sapiens about 250,000 years ago.

Then, 200,000 years ago, came the second-to-last glacial period: the Wolstonian. This lasted until about 130,000 years ago. Then came a warm period called the Eemian, which lasted until about 110,000 years ago. During the Eemian, Neanderthalers hunted rhinos in Switzerland! It was a bit warmer then that it is now, and sea levels may have been about 4-6 meters higher—worth thinking about, if you’re interested in the effects of global warming.

The last glacial period started around 110,000 years ago. This is called the Winsconsinan or Würm period, depending on location… but let’s just call it the last glacial period.

A lot happened during the last glacial period. Homo sapiens reached the Middle East 100,000 years ago, and arrived in central Asia 50 thousand years ago. The Neanderthalers died out in Asia around that time. They died out in Europe 35 thousand years ago, about when Homo sapiens got there. Anyone notice a pattern?

The oldest cave paintings are 32 thousand years old, and the oldest known calendars and flutes also date back to about this time. It’s striking how many radical innovations go back to about this time.

The glaciers reached their maximum extent around 26 to 18 thousand years ago. There were ice sheets down to the Great Lakes in America, and covering the British Isles, Scandinavia, and northern Germany. Much of Europe was tundra. And so much water was locked up in ice that the sea level was 120 meters lower than it is today!

Then things started to warm up. About 18 thousand years ago, Homo sapiens arrived in America. In Eurasia, people started cultivating plants and herding of animals around this time.

There was, however, a shocking setback 12,700 years ago: the Younger Dryas episode, a cold period lasting about 1,300 years. We talked about this in “week304”, so I won’t go into it again here.

The Younger Dryas ended about 11,500 years ago. The last glacial period, and with it the Pleistocene, officially ended 10,000 years ago. Or more precisely: 10,000 BP. Whenever I’ve been saying ‘years ago’, I really mean ‘Before Present’, where the ‘present’, you’ll be amused to learn, is officially set in 1950. Of course the precise definition of ‘the present’ doesn’t matter much for very ancient events, but it would be annoying if a thousand years from now we had to revise all the textbooks to say the Pleistocene ended 11,000 years ago. It’ll still be 10,000 BP.

(But if 1950 was the present, now it’s the future! This could explain why such weird science-fiction-type stuff is happening.)

As far as geology goes, the Holocene is a rather silly epoch, not like the rest. It’s just a name for the time since the last ice age ended. In the long run it’ll probably be called the Early Anthropocene, since it marks the start of truly massive impacts of Homo sapiens on the biosphere. We may have started killing off species in the late Pleistocene, but now we’re killing more—and changing the climate, perhaps even postponing the next glacial period.

Here’s what the temperature has been doing since 12000 BC:

Finally, here’s a closeup of a tiny sliver of time: the last 2000 years:

In both these graphs, different colored lines correspond to different studies; click for details. The biggish error bars give people lots to argue about, as you may have noticed. But right now I’m more interested in the big picture, and questions like these:

• Why was it so hot in the early Eocene?

• Why has it generally been cooling down ever since the Eocene?

• Why have temperature fluctuations been growing since the Miocene?

• What causes the glacial cycles?

For More

Next time we’ll get into a bit more detail. For now, here are some fun easy things to read.

This is a very enjoyable overview of climate change during the Holocene, and its effect on human civilization:

• Brian Fagan, The Long Summer, Basic Books, New York, 2005. Summary available at Azimuth Library.

and I urge you to check out this website for a nice visual tour of the Earth’s history.

Finally, I thank Frederik de Roo and Nathan Urban for suggesting improvements to this issue. You can see what they said on the Azimuth Forum. If you join the forum, you too can help write This Week’s Finds! I could really use help from earth scientists, biologists, paleontologists and folks like that: I’m okay at math and physics, but I’m trying to broaden the scope now.

We are at the very beginning of time for the human race. It is not unreasonable that we grapple with problems. But there are tens of thousands of years in the future. Our responsibility is to do what we can, learn what we can, improve the solutions, and pass them on. – Richard Feynman

I’m not sure which graph you’re referring to, but no matter which one you mean, this issue is important. I need to learn more about climate proxies. When I do, I’ll be able to give you better answers. But here’s what I can say now. I hope someone more knowledgeable can add detail.

Of course people want to use as many proxies as possible, but there are fewer proxies available as we go further back in time. But if you look at this list, you’ll get a bit of a feeling for the issue. For example, the oldest ice core, EPICA, goes back only 800,000 years.

When we go back about 5 million years, it seems the main proxy we have is changes in oxygen-18 concentrations in benthic foraminifera:

I bet other proxies have been investigated, but I don’t know if any are considered reliable this far back. And if you click on this graph, you’ll see quite elaborate data processing was used to produce it: they took sediment samples from 57 different locations and correlated them assuming the fluctuations were synchronized with the Milankovitch cycles in the Earth’s orbit!

We need to do something like this because sediments are deposited at different rates at different locations and times. But clearly it’s a tricky business: if you’re not careful, you can fool yourself into seeing patterns that aren’t there! It would be nice to investigate the procedure that was done, and see how convincing it seems. It could be a fun nontrivial exercise in data analysis.

Maybe someone can tell me what’s known about this puzzle. Suppose you have a bunch of wiggly graphs

and you want the wiggles to become highly correlated when you reparametrize the time coordinates , but you don’t want to allow yourself to reparametrize the time coordinates ‘too much’, since that’s cheating. What’s a good algorithm for doing this? You’re trying to maximize some sort of correlation while imposing a penalty for reparametrizing the time coordinates in too wiggly a way.

Anyway:

For the last few glacial cycles we can measure more things, so we can be more confident that we know what’s happening. This graph shows the amount of deuterium in Vostok and EPICA ice core samples, and also changes in the amount of oxygen-18 in foraminifera (that’s the graph labelled ‘Ice Volume’):

We can also measure the amount of CO2 in the air bubbles in the ice cores, and that turns out to be closely correlated to the temperature, though sometimes it leads or lags the changes in temperature.

Maybe someone can tell me what’s known about this puzzle. Suppose you have a bunch of wiggly graphs

and you want the wiggles to become highly correlated when you reparametrize the time coordinates , but you don’t want to allow yourself to reparametrize the time coordinates ‘too much’, since that’s cheating. What’s a good algorithm for doing this? You’re trying to maximize some sort of correlation while imposing a penalty for reparametrizing the time coordinates in too wiggly a way.

Over on the Forum, Graham Jones pointed out that this problem is called dynamic time warping! And apparently many algorithms for dynamic time warping are available in R. So we could try this.

In radiocarbon dating the procedure of correlating “wiggles” in 14C age and calendar age is actually called “wiggle matching” in the literature. I think the term may generalize to matching proxy data to orbital cycles (part of the field of cyclostratigraphy). There appears to be a bit of an art to it – I’m not sure if fully automated algorithms are in use.

I’ve been interested in how to do this as well, but I’ve never found the time to get into it. I might be tempted to infer a functional mapping using a slowly-varying Gaussian process prior on the reparameterization. I think that’s how Caitlin Buck does it for radiocarbon dating.

The question is if there is any math that could help here – pattern matching for this kind of time series would certainly be done using hidden Markov models, like in speech recognition. Speech recognition seems to have a lot in common with cyclostratigraphy.

Mathematics is about careful explanations of how geniuses achieve success, why it works and why you don’t have to be a genius yourself to apply their wisdom. In short, mathematics is about turning art into algorithms.

I’m sure there is math that would help, and I’m sure that it could be substantially automated with sufficient work. As I mentioned above, a Gaussian approach process might work, and so could the HMM approach you suggest.

(On the other hand, my experience with applied statistics is that there is still usually a need for exploratory analysis with human input before turning the algorithm loose on data … I’m not entirely in the “black-box machine learning” camp.)

“In short, mathematics is about turning art into algorithms.” I often say statistics is about quantifying your intuition … expressing mathematically how sure you are about whatever process generated your data.

There are other temperature proxies besides oxygen-18. One I frequently see for deep sea ocean cores (tens of millions of years ago) is magnesium/calcium (Mg/Ca) ratios in foraminifera. The absorption of these elements by plankton into their shells depends on the temperature of seawater in which they reside. I’m not too finely versed on the pros and cons of different proxies, but I know that oxygen-18’s temperature response can get confounded with ice volume and ocean salinity changes. I sometimes also see TEX86, a biological temperature proxy. These proxies are not as commonly available as oxygen isotopes, however. They have their own confounders, but the hope is that you can try to control for them indirectly by using multiple proxies.

I would worry that a biology-based temperature proxy could have a slow systematic change (or worse, a slow change correlated to other factors) due to evolution. Is there any way to test whether this may have happened?

This is a hard problem. Paleoclimate analyses often assume that there are no systematic changes in how biological proxies respond to temperature due to evolution. This isn’t because such changes are logically impossible, but simply because we don’t have much evidence to tell us how they could change.

There are a few things that can be done. It is known that biological temperature proxies can have species-dependent “vital effects”. It stands to reason that the evolution of species can effect their response to temperature.

It may be possible to bound this effect: we can look at the variation of vital effects between modern species, and assume that the variation of vital effects within a species over time is smaller than this (on the grounds that if the time variation is large, it may have become a new species by now).

Under this assumption, it’s possible to use temperature proxies of species that were extant in the past and are still extant today. It’s still possible (in fact, certain) for evolution to have occurred between the ancient and modern populations of the species, but maybe the effect isn’t as large as the between-species variation.

Another approach is to try to use proxies where vital effects (at least in modern species) aren’t as significant, so they’re more “pure” indicators of environmental conditions.

This can be extended to use multiple types of proxies, on the grounds that if there were systematic evolutionary variations, they wouldn’t be expected to affect all proxies in the same way.

I suppose you might also get into the evolutionary genetics of the problem, rebuilding phylogenetic trees and inferring genomic change, to see if the ancient species were likely to have had different genes affecting whatever controls the temperature proxy (e.g., the biological fractionation process). I don’t think anybody has done this, to my knowledge.

None of these assumptions are airtight, but there are at least a few basic consistency checks, and I think people will continue to make the “no significant evolutionary change” assumption unless there’s evidence for really wide interspecies or multiproxy divergences.

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You need the word 'latex' right after the first dollar sign, and it needs a space after it. Double dollar signs don't work, and other limitations apply, some described here. You can't preview comments here, but I'm happy to fix errors.